Problem: A certain factory produces and sells $C$ computers per month. It costs $x$ dollars to produce a single computer, and the factory sells each computer for $y$ dollars. Their monthly net profit is $10{,}000$ dollars. Write an equation that relates $C$, $x$, and $y$.
The factory's net profit is equal to the factory's total income, reduced by the factory's total expenses. What is the factory's income from producing and selling $C$ computers? What are the expenses? The income is $Cy$ dollars: $\begin{aligned} &\phantom{=}\left(y\,\dfrac{\text{dollars}}{\text{computer}}\right)\left(C\,\text{computers}\right) \\\\ &=Cy\,\dfrac{\text{dollars}}{\cancel\text{computer}}\cdot\,\cancel\text{computers} \\\\ &=Cy\,\text{dollars} \end{aligned}$ Similarly, the expenses are $Cx$ dollars. The net profit is then $Cy$ minus $Cx$ : $Cy-Cx=10{,}000$ This can also be written as $C(y-x)=10{,}000$.